Resolution issue b/w monitors and Internet

Question

I've been working on some night photos I took of the northern lights and I've run into an issue.  After doing my usual processing with Photoshop my pictures look the way I'd like them to on my desktop monitor.  I then do my usual Convert to Profile--Working RGB-SrGB and then Save for Web, followed by uploading them to the Internet.  When I view these particular photos on the Internet on my monitor they look awful.  The colors look grainy and unnatural and the photos have noise in the detail.   I have spent hours running them through noise filters and making other changes.  They will always look good in Photoshop and then terrible on-line.  Then I decided to view them on my iPad and found that they look good!  I don't think it's the desktop monitor resolution because they look good in Photoshop on the same monitor.  Does anyone have any idea as to why they look terrible on-line on the desktop monitor but good on my iPad?  I'm at a loss here.
The  Profile is:
Settings: North America General Purpose 2
RGB: sRGB
CMYK: US Web Coated(SWOP) v2
Gray: Dot Gain 20%
Spot: Dot Gain 20%
Color Management Policies:
RGB: Preserve Embedded Profiles
CMYK: Preserve Embedded Profiles
Gray: Preserve Embedded Profiles
Here's an example of one of the photos:

Answer 1

The image posted in this thread, above, and at the smugmug link given, are both tagged with the sRGB IEC61966-2.1 color profile.  That's fine.
But...
The color values in the images are significantly different.  The image you posted at the smugmug.com web site is a good bit lighter than in the image posted in this thread.  That implies you either processed the image differently or reprocessed it between saving those two versions.
Specifically, redgreen2.jpg is lighter than redgreen7.jpg.
It's a bit hard to diagnose an issue when there's a moving target.
Can you describe exactly what you did between those two images?  Perhaps the problems you're seeing with differences are because of something you're inadvertently doing.  It crossed my mind that you may be looking at two different images and making the assumption that they should be the same.
-Noel